Google Operating System noticed that Google will increase the width of the search box if your query is long enough to warrant a wider search box. Note that Google does not expand the search box as you type. It only happens after you search.
I measured Google’s search box on my Safari browser at the smallest size of 295 pixels wide, then 425 pixels wide and at its largest, 495 pixels wide. By contrast, Yahoo is 330 pixels wide and Live Search is 390 pixels wide, and both do not expand.
Here are screen captures of Google from smallest to largest (note, the images are resized; click on them to see the full size image):
Now let’s compare Google’s smallest to Yahoo and Live Search’s standard size on Safari:
Postscript: Yahoo seemed to have redesigned their home page, making the search box more prominent by placing the Yahoo logo directly above it. Google Blogoscoped has screen captures of older Yahoo designs.